Most household and construction debris is fine to load. The limits come from Florida's landfill rules and from the facility that takes your load.
Florida law keeps car batteries, used oil, and large appliances like refrigerators and washers out of landfills. Whole tires can't be buried either, and yard trash has its own rules at lined landfills. Rechargeable batteries need to be recycled.
Beyond the state rules, hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster.
The City's McKay Bay disposal page also lists what that site will never accept. The list includes wet drywall mud, bricks, rocks, cinder blocks, dirt, fuel and motor oil, propane tanks, fluorescent bulbs, and electronics. Keep those out of a mixed load, or ask us about a separate container for heavy material.
If you're unsure about an item, ask your account manager before you load it.